Glueballs are investigated through gluonic operators on two   $ N_f=2+1 $   RBC/UKQCD gauge ensembles at the physical pion mass. The statistical errors of glueball correlation functions are considerably reduced through the cluster decomposition error reduction (CDER) method. The Bethe-Salpeter wave functions are obtained for the scalar, tensor, and pseudoscalar glueballs by using spatially extended glueball operators defined through the gauge potential   $ N_f=2+1 $   in the Coulomb gauge. These wave functions exhibit similar features of non-relativistic two-gluon systems and are used to optimize the signals of the related correlation functions at the early time regions, where the ground state masses are extracted. These masses are close to those from the quenched approximation and indicate the possible existence of glueballs at the physical point. The resonance feature of glueballs and the mixing with conventional mesons and multi-hadron systems should be considered in a more systematic lattice study.